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cosine_function [2014/01/29 19:49]
nikolaj
cosine_function [2014/03/21 11:11] (current)
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 ===== Cosine function ===== ===== Cosine function =====
 ==== Function ==== ==== Function ====
-| @#FFBB00: $\mathrm{\cos}:​ \mathbb C\to\mathbb C$ | +| @#FFBB00: definiendum ​| @#FFBB00: $\mathrm{\cos}:​ \mathbb C\to\mathbb C$ | 
-| @#FFBB00: $\cos(z) := \sum_{k=0}^\infty \frac{(-1)^{k}}{(2k)!}z^{2n} $ |+| @#FFBB00: definiendum ​| @#FFBB00: $\cos(z) := \sum_{k=0}^\infty \frac{(-1)^{k}}{(2k)!}z^{2n} $ |
  
 ==== Discussion ==== ==== Discussion ====
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 ^ $\cos(\theta) = \frac{1}{2}(\mathrm e^{i\theta}+\mathrm e^{-i\theta}) $ ^ ^ $\cos(\theta) = \frac{1}{2}(\mathrm e^{i\theta}+\mathrm e^{-i\theta}) $ ^
  
-i.e. if $\zeta_\theta:=\mathrm e^{i\theta}$,​ then $\frac{1}{2}(\zeta_\theta+\overline{\zeta_\theta})=\cos(\theta)$.+i.e. if $\zeta:=\mathrm e^{i\theta}$,​ then $\zeta+\overline{\zeta}=2\cos(\theta)$.
 ==== Parents ==== ==== Parents ====
-=== Requirements ​===+=== Context ​===
 [[Infinite sum of complex numbers]], ​ [[Infinite sum of complex numbers]], ​
 [[Factorial function]] [[Factorial function]]
 === Related === === Related ===
 [[Exponential function]], [[Sine function]] [[Exponential function]], [[Sine function]]
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